Expansion of a Plasma Shell into a Vacuum Magnetic Field

The problem of an initially spherical, superconducting plasma shell expanding into an ambient uniform magnetic field is solved by approximate analytic and numerical methods. The solution is found to depend on only one parameter, the ratio of the initial kinetic energy of the plasma to the magnetic energy initially displaced by the plasma. The dependence of the solutions on this parameter is studied. A criterion for the stability of the solutions is given.